Here's a suggested itinerary for 5 days in New York:

Day 1:

• Start your day with a visit to the iconic Statue of Liberty and Ellis Island. Take a ferry ride from Battery Park to Liberty Island and enjoy the stunning views of the city skyline.
• After returning to Manhattan, head to the One World Observatory for breathtaking panoramic views of the city.
• In the evening, catch a Broadway show or explore the vibrant Times Square.

Day 2:

• Begin your day by visiting the Metropolitan Museum of Art, one of the world's largest and most comprehensive art museums.
• After lunch, take a stroll through Central Park and enjoy the beautiful scenery.
• In the evening, head to the Top of the Rock Observation Deck for stunning views of the city at night.

Day 3:

• Start your day by exploring the trendy neighborhoods of SoHo and Greenwich Village, known for their unique shops, cafes, and restaurants.
• After lunch, visit the 9/11 Memorial and Museum to pay tribute to the victims of the tragic events of September 11th.
• In the evening, take a walk across the Brooklyn Bridge and enjoy the stunning views of the city skyline.

Day 4:

• Begin your day by visiting the famous Empire State Building and taking in the breathtaking views of the city from the observation deck.
• After lunch, explore the bustling streets of Chinatown and Little Italy.
• In the evening, catch a game at Madison Square Garden or explore the trendy Meatpacking District.

Day 5:

• Start your day by visiting the iconic Grand Central Terminal and admiring its stunning architecture.
• After lunch, take a ferry to the Statue of Liberty and Ellis Island for a closer look.
• In the evening, head to the Rockefeller Center for ice skating and holiday festivities during the winter months, or explore the High Line park during the warmer months.

Of course, this is just a suggested itinerary and there are countless other things to see and do in New York City. Have a great trip!